MTH101
GEOMETRY
This sample unit outline is provided by CHC for prospective and current students to assist
with unit selection.
Elements of this outline which may change with subsequent offerings of the unit include
Content, Required Texts, Recommended Readings and details of the Assessment Tasks.
Students who are currently enrolled in this unit should obtain the outline for the relevant
semester from the unit lecturer.
Unit code
MTH101
Unit name
Geometry
Associated higher
education awards
Diploma of Liberal Arts: Foundations of Learning
Bachelor of Arts in the Liberal Arts
Duration
One semester
Level
Introductory
Unit Coordinator
To be advised
Core/Elective
Core
Weighting
Unit credit points:
10 credit points
Total course credit points:
Student workload
Face-to-face on-site
Timetabled hours
Personal study hours
80 credit points
240 credit points
PL
E
Diploma of Liberal Arts: Foundations of Learning
Bachelor of Arts in the Liberal Arts
Total workload hours
39
111
150
M
Students requiring additional English language support are expected to undertake an additional one
hour per week.
In order to be considered for a passing grade, students must attend at least 80% of class sessions.
Face-to-face on-site
Pre-requisites/
Co-requisites/
Restrictions
Nil
Rationale
This unit (along with SCI101 and MUS101) initiates students into a key subject of the traditional
quadrivium, which is essentially the study of pattern, harmony, symmetry and order in nature and
mathematics, viewed as a reflection of the Divine Order. Thomas More argued, “There are some
who through knowledge of things natural construct a ladder by which to rise to the contemplation of
things supernatural.” That is a goal of this unit in relation to the progression of the larger curriculum.
SA
Delivery mode
Throughout the history of Western civilisation, geometry has influenced philosophers (including
Plato, Aristotle, Descartes, Spinoza, and Kant), both in seeming to have achieved truth and in having
found a method of proving truths. Plato wrote, “Geometry will draw the soul toward truth and
create the spirit of philosophy.” Here he points to some of the many benefits of geometry for
preparing students for later philosophical thought. Studying geometry helps to teach and train
students in deductive logic, precision and certainty, and complex abstract thought.
This unit trains students in the art of geometry according to the method of Euclid. Students work
through Euclid’s Elements, discussing the principles and definitions proper to geometry. Students
concentrate on learning the nature of proof by examining Euclid’s theorems and presenting them in
class. Students also explore the basic mathematical work of Descartes and Newton not only to
learn mathematical skills but also to consider the ways in which mathematical thought has
influenced, and been influenced by, the broader Western tradition.
MTH101 Geometry
Page 2 of 4
CRICOS Provider Name: Christian Heritage College
1 February 2016 (Sample)
CRICOS Provider Number: 01016F
This is not a version-controlled document when printed
Author: Millis Institute
Authorised: Academic Board
www.chc.edu.au
Prescribed text(s)
Euclid 2002, Euclid’s Elements, ed. D Densmore, trans. T Heath, Green Lion, Ann Arbor, MI.
Recommended
readings
Boyer, C & Merzbach, U 2011, A History of Mathematics, 3rd edn, Wiley, Hoboken, NJ.
Descartes, R 2001, Discourse on Method, Optics, Geometry, and Meteororology, trans. P Olscamp,
Hackett, Indianapolis, IN.
Dunham, W 1991, Journey Through Genius: The Great Theorems of Mathematics, Penguin,
Middlesex, UK.
Katz, V 2008, A History of Mathematics, 3rd edn, Pearson, Essex, UK.
Newton, I 1999, The Principia: Mathematical Principles of Natural Philosophy, trans. B Cohen, & A
Whitman, University of California, Berkeley, CA.
Specialist
resources
requirements
Nil
Content
1. Introduction, Math in historical context
PL
E
2. Foundational Elements, Pythagoreans, the Parallel Postulate
3. Euclid, Propositions 1-5: Triangles, SAS
4. Propositions 6-10: Isosceles Triangles, Bisection, SSS
5. Propositions 11-20: Perpendicular Construction, Right Angles
6. Propositions 21-25: Triangle Constructions, Angle Constructions, Linear Properties of Triangles
7. Propositions 26-30: ASA, SAA, Parallel Lines
8. Propositions 31-45: Parallelograms and Constructions
M
9. Propositions 46-48: Pythagorean Theorum
10. Descartes, Discourse on Method (Parts 2, 4)
11. Descartes, Geometry, Book I
SA
12. Newton’s Calculus (selections)
Learning outcomes
On completion of this unit, students will have:
1. Understood the basic concepts of formal plane Euclidean geometry, including proofs of
similarity and congruence theorems, areas and volumes, and the parallel postulate;
2. Understood and defined properties of two and three-dimensional geometric shapes;
3. Acquired the ability to recognize the difference between formal proofs and informal
justifications and apply geometric knowledge to construct logical arguments/formal proofs;
4. Acquired the ability to use a variety of problem solving strategies and inductive and deductive
reasoning skills to solve geometric problems;
5. Developed the capacity to explain mathematical observations and conjectures orally and in
written reports using standard English and appropriate mathematical language;
6. Gained insight into the development of geometry from a historical perspective including a study
of some of the mathematicians that contributed to it;
7. Placed the different mathematical worlds of Euclid, Descartes, and Newton in the narrative of
both the Christian and the Western tradition; and
8. Communicated at an appropriate tertiary standard with special attention to correct grammar,
punctuation, spelling, vocabulary, usage, sentence structure, logical relations, style, referencing
and presentation.
MTH101 Geometry
Page 3 of 4
CRICOS Provider Name: Christian Heritage College
1 February 2016 (Sample)
CRICOS Provider Number: 01016F
This is not a version-controlled document when printed
Author: Millis Institute
Authorised: Academic Board
www.chc.edu.au
Assessment tasks
Task 1: In-Class Quizzes
Word Length/Duration:
3 x 45 minutes each
Weighting:
60% (20% each)
Learning Outcomes:
1-4, 6
Assessed:
Weeks 5, 7, 10
Task 2: Euclid Presentations
Word Length/Duration:
5 minutes
Weighting:
10%
Learning Outcomes:
1-3, 5
Assessed:
Weeks 3-9
Task 3: Euclid Paper
1,000 words
Weighting:
15%
Learning Outcomes:
1, 5-7
Assessed:
PL
E
Word Length/Duration:
Week 10
Task 4: Pythagorean Theorem Paper
Word Length/Duration:
1,200 words
Weighting:
15%
Learning Outcomes:
Assessed:
Week 14
M
This unit helps to reveal the harmony of mathematical order in creation by training students in the
art of Euclidean geometry. Students work through Euclid’s Elements, discussing the principles and
definitions proper to geometry and learning the nature of proof.
SA
Unit Summary
1, 3-7
MTH101 Geometry
Page 4 of 4
CRICOS Provider Name: Christian Heritage College
1 February 2016 (Sample)
CRICOS Provider Number: 01016F
This is not a version-controlled document when printed
Author: Millis Institute
Authorised: Academic Board
www.chc.edu.au